At a price of $p the demand x per month (in multiples of 100) for a piece of software is:
x^2 +2xp +2p^2 =500
The manufacturer is increasing the price at a rate of 20 cents per month. Find the corresponding rate of decrease in demand for the software when the software costs $10.
dp/dt= 20 cents/month
p=10
dx/dt=?
x=?
Because x was not given I plugged in dp/dt and p into the original equation, plugged it into the quadratic formula and came up with x= 10.
Then I took the derivative of the original eq:
2x(dx/dt)+2(x(dp/dt)+p(dx/dt))+4p(dp/dt)=0
And I plugged everything else in and came up with dx/dt=30
Did I solve this correctly? Should I have put .20(dollars/month) instead of 20 (cents/month)?
Thanks!